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Lesson Video: Frequency Tables Mathematics

In this video, we will learn how to construct, read, and interpret frequency tables for a given qualitative data set.

10:07

Video Transcript

In this video, we’ll learn how to construct, read, and interpret frequency tables for a qualitative data set. We’ll also learn how to find the mode from a frequency table. We can begin by recapping that the word “frequency” simply means the number of times a data value occurs. We can put these data values along with the frequencies into a frequency table. In the first example, we’ll see how we can create a frequency table.

Using the given data for school performance, complete the frequency table.

If we look at the top section of this table, we can see that there are words, for example, weak or good, relating to school performance. We don’t know whether this is for one student or for a group of students. But what we need to do here is create a way to organize this jumble of information. The way that we can do that is by filling in the missing spaces at the bottom of this table.

We need to find the frequency for each category of school performance and to find the frequency that’s just the total for every data value. We can do this in two ways. If we don’t have a very large data set like here, we could take the category of “very weak” and go through the table, counting how many we have. As there are four different occurrences of “very weak,” then the frequency of “very weak” would be four.

Another method which is useful for large data sets is to use a tally. The first data value here is “weak,” so we would add that to the tally, next add good school performance, then another occurrence of “weak.” And then we could continue going through the table. We then need to update our frequency totals. The data value of “pass,” which had no tally, would get a zero frequency. We see that the value of four for the very weak school performance is also clarified with the tally of four.

A very good check at this point is to count the number of different data values that we had originally. We have four rows of five columns, which would give us 20 data values. And we would therefore check that our total frequency is also equal to 20. And it would indeed be 20. We can therefore give our answer that our missing frequency values are four, five, zero, three, six, and two.

In the next question, we’ll see how we can interpret a frequency table.

The table shows the number of students in a class that play different sports. What is the least popular sport in class?

In the frequency table below, we have a number of different games and the number of students that play those types of games in this particular class. The value of 16 is the frequency or number of students that play football. This means that 12 students will play volleyball, four students play handball, and eight students will do swimming.

The least popular sport that we’re asked for will mean the fewest number of students doing it. We can also think of this as the game which has the lowest frequency. When we look at the table, the lowest frequency here is four. But be careful as that’s not the answer. The answer would in fact be handball as we want to give the sport and not the lowest value. Therefore, handball is the least popular sport in this class.

We’ll now look at another similar question type, only this time our frequency table will be about TV programs.

The table shows the genres of TV programs watched by students in a class. Which program is the most popular?

The frequency table in this question lists the different types of TV program, along with the number of students that watched each type. We could say therefore that three students watch sitcoms, 13 watch game shows, nine watch talk shows, five watch dramas, and four watch sports programs. We’re asked to interpret this table to work out which TV program is the most popular. The most popular program will be the one that has the highest frequency, in other words, the highest number of students watching each program. The highest number of students in this table is the value of 13. So our answer for the most popular program is therefore the game show.

In the following question, we’ll see how we can find the mode from a frequency table.

The table shows the marks that 30 students attained in an examination. Find the mode mark.

The first row in this table gives us the different marks or scores that students achieved in the examination. The second row tells us how many students achieved each of these marks. Therefore, we could say that five students achieved a mark of five, seven students achieved a mark of six, and so on. We’re asked here to find the mode mark. So let’s remember what we mean by the mode.

The mode is the most frequently occurring value. Now, we might easily be able to find this with a data set, but perhaps not so easily with a frequency table. Let’s take our five students who achieved a mark of five. If we wrote this in a list, we’d have five of the number fives. Continuing this list, we’d have seven students achieved a mark of six, so we’d have seven number sixes. We could continue this list, which would show individually every mark that these students attained. This is also a nice illustration that the total number of students we could see would be equal to 30.

So let’s go back to how we would find the mode from this list. The most common value here must be the value of six as there’s seven sixes in this list. You might notice that of course we could’ve done this from our original frequency table simply by looking for the value that has the highest frequency. The highest frequency is the largest number of students, which is seven, which means that the answer for the mode mark must be six, as that’s the data value that our frequency of seven would represent.

In the final question, we’ll see how we can interpret a two-way frequency table.

This table shows the area in thousands of hectares of land used for growing different crops in a country from 2001 to 2005. Did the total area of land used for growing crops increase or decrease from 2001 to 2002? By how many hectares did it increase or decrease?

If we take a look at this frequency table, we can see on the different rows we have the different crop types and the different columns show us five different years. This is in fact what we might call a two-way frequency table. Let’s take a look at this first data value. We have the wheat crop in 2001 and the digits two three four one. We know that this value of 2,341 represents the area of land used for growing the crop of wheat. However, if we read the details carefully, we can see that this area is in fact thousands of hectares. So our value would be 2,341 thousand or rather 2,341,000 thousand.

Knowing that these values are in thousands of hectares will be important when we come to answering the question. The question asks if the total area of land between 2001 and 2002 increased or decreased. This means that, instead of any particular crop, we’re looking for the total crop. And we’re only really interested in two years, 2001 and 2002.

To calculate the total crop in 2001, we’d need to add up all the frequencies for wheat, beans, barley, clover, beet, and vegetables in this column, which gives us the value of 6,376 thousand hectares. We can calculate the total crops in 2002 by using the same method. This gives us the value of 6,291. The first part of this question asks if the total area of land increased or decreased from 2001 to 2002. As this value has got smaller, we could say that the total must have decreased.

To answer the second part of this question, we’ll need to subtract. We can find the difference or how much it decreased by calculating 6,376 subtract 6,291, giving us an answer of 85. We must remember though that this value of 85 would in fact be 85,000 hectares. So our final answer is that it decreased by 85,000 hectares.

We can now summarize what we’ve learnt in this video. We began by recapping that frequency is the number of times a data value occurs. A frequency table is a method of organizing data values together with their frequencies. And finally, we saw how we can find the mode from a frequency table by finding the data value with the highest frequency.

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